"Tumor-Induced Angiogenesis Model"[unreadable] We have developed a model of tumor-induced angiogenesis that includes the migratory response of endothelial cells (ECs) to tumor angiogenic factors, and the interaction of ECs with the extracellular matrix (ECM). ECs switch between growth, differentiation, motility, or apoptotic behavior in response to the local topology and composition of the ECM. Considering the ECM as a statistically inhomogeneous two-phase random medium, we have shown that the ECM can be a natural barrier to angiogenesis. We have studied vascular network formation for several ECM distributions and topologies and have found a correlation with percolation. A threshold exists, under which sprouts cannot reach the tumor. During the growth of the vascular network, a competition exists between the attraction exerted by the tumor and the preferred path created by the ECM. [unreadable] [unreadable] We have also examined the influence of branching on tumor vascularization. Branching is a natural phenomenon which helps the tumor become vascularized. By increasing the number of sprouts (i.e. capillaries), the vascular network increases the probability of reaching the tumor, as it can explore more pathways. Our simulations have shown that after two branching events, the vascular network is very likely to reach the tumor.[unreadable] [unreadable] "Quantitative assay to study cell trajectory and morphology in highly oriented collagen fibers"[unreadable] In collaboration with Dr. Anne Plants group at NIST who has designed thin films of highly oriented collagen fibers, we have studied the local adhesion and orientation of ECs along collagen fibers. First, by using Fourier transform and Pearson correlation analysis, we were able to assess the fiber orientation. Then an eccentricity model for cell orientation and morphology was used to study cell trajectory and shape, and their correlation with the orientation of collagen fibers. High degrees of correlation have been found, suggesting that this method can be used to study cell migrations in a controlled environment [unreadable] [unreadable] We are continuing our studies to characterize the physical and chemical proprieties of the ECM with fluorescence correlation spectroscopy (FCS). By measuring the diffusion coefficient of fluorescent molecules in ECM gels, FCS is able to measure the degradation of the gel by matrix metalloproteases (MMPs) released by cells. The interaction and stress generated between ECs and the ECM will also be measured.[unreadable] [unreadable] "Directional Guidance by Growth Factor Gradients in Angiogenesis"[unreadable] The process of tumor-induced angiogenesis, in which a growing tumor recruits new vasculature to increase nutrient intake, is a crucial part of tumor growth. For tumors larger than approximately 1 mm, diffusion of oxygen and other nutrients from nearby capillaries is insufficient to sustain their growth. The tumor cells become hypoxic and secrete a growth factor called Vascular Endothelial Growth Factor (VEGF). The uptake of this growth factor by endothelial cells on nearby capillaries initiates a sequence of events that lead to the formation of a capillary network around the tumor. In addition to delivering nutrients that facilitate further tumor growth, the capillary network also provides a means for the tumor to metastasize. Because tumor-induced angiogenesis is crucial to tumor lethality, considerable research has been devoted to disrupting this process, for the purpose of preventing metastasis and starving the tumor. Particular attention has been paid to therapies that target VEGF molecule.[unreadable] [unreadable] There are open questions concerning which form of VEGF is most important in the process of angiogenesis, the role that each form plays, how the different forms of VEGF interact with the extracellular matrix (ECM), and how the different forms of VEGF interact with matrix metalloproteases (MMPs) to control the process of tumor-induced angiogenesis. Due to alternative splicing, VEGF can be produced in isoforms with 120, 165, 189, or 206 amino acids. The iso form VEGF120 does not bind to the ECM and hence diffuses freely, VEGF189 and VEGF206 bind rapidly to the ECM and hence do not travel far before binding, and VEGF165 is an intermediate form that binds slowly to the ECM and hence travels longer distances before binding. The matrix-bound isoforms of VEGF can all be cleaved from the ECM by MMPs, in particular MMP2 and MMP9, releasing a slightly smaller molecule VEGF110 that can diffuse through the ECM. All of the various isoforms (120, 165, 189, 206, matrix-bound, and 110) can bind to the receptors responsible for mitogenic and chemotactic effects in endothelial cells, although it is known that VEGF120 and VEGF110 have weaker chemotactic effects.[unreadable] [unreadable] Since gradients of growth factors are necessary to guide chemotactic migration of cells and pattern the vasculature, we have devised a system of reaction-diffusion equations that model the diffusion, binding, and cleavage of different VEGF isoforms in the extracellular matrix around a tumor. Our model has 3 adjustable parameters:[unreadable] [unreadable] 1) The rate constant for binding to the extracellular matrix: This parameter varies depending on the isoform under consideration.[unreadable] 2) The rate of VEGF production: This parameter is known to vary in vivo, depending on the type of tumor, degree of hypoxia, and a variety of other conditions, and is a target for pharmacological interventions.[unreadable] 3) The rate of MMP production by cells proximal to capillaries: This parameter is also known to vary in vivo, and can be regulated by medications and naturally occurring tissue inhibitors of metalloproteases (TIMPs).[unreadable] [unreadable] We find in our simulations that rapid binding to the extracellular matrix leads to very short-range gradients of matrix-bound VEGF, whereas slower binding leads to much longer-range gradients of matrix-bound VEGF. This is consistent with several in vivo studies, which have found that the vasculature surrounding tumors that produce VEGF189 is very disorganized when compared with the vasculature surrounding tumors that produce VEGF165. Vessels feeding tumors that express VEGF165 tend to be somewhat tortuous but still proceed toward the tumor, suggesting the presence of some sort of directional cue. Vessels feeding tumors that express VEGF189, on the other hand, tend to meander in a random walk before reaching the tumor, suggesting the absence of some sort of directional cue. Our simulations elegantly explain this difference in morphology as being due to the presence or absence of a strong gradient to guide endothelial cell migration.[unreadable] [unreadable] Our simulations also sheds light on the role of cleaved VEGF molecules. Because MMPs are expressed by cells adjacent to capillaries rather than by tumor cells, the fastest release of cleaved VEGF occurs near capillaries rather than near the tumor, and gradients of cleaved VEGF would tend to guide cell migration toward the capillary rather than toward the tumor. This strongly suggests that the biological role of cleaved VEGF165 is primarily mitogenic rather than chemotactic.[unreadable] [unreadable] In addition, our calculations shed light on a key role of MMPs in tumor-induced angiogenesis: Without MMPs, the ECM would become saturated with matrix-bound VEGF, resulting in a uniform concentration profile. If the concentration profile is uniform then there is no gradient and hence no directional cue to guide endothelial cell migration. This is consistent with the finding that MMP9 release is necessary to trigger the onset of tumor-induced angiogenesis.